Speaker: 王国芳教授，德国弗莱堡大学

Inviter: 周向宇院士

Title: New optimal Sobolev inequalities

Language: Chinese

Time & Venue: 2025.03.11 20:10-21:10 南楼N913

Abstract: The optimal Sobolev inequality is very important in analysis, especially in the resolution of the Yamabe problem. It has many generalizations, especially to higher order and to fractional order Sobolev inequalities. The optimal Sobolev inequality can also be viewed as an isoperimetric inequality between the total scalar curvature and the volume of a conformal metric. In the talk we will propose a new type Sobolev inequality, which is an isoperimetric inequality relating total higher order Q curvatures. We prove one special case, which already leads to a new Yamabe type problem. At the end I will address this new Yamabe problem. This is a joint work with Yuxin Ge (Toulouse) and Wei Wei (Nanjing and Freiburg).